First slide

Radiation

Question

Equal volumes of water and alcohol when put in similar calorimeters take 100 sec and 74 sec respectively to cool from $50^{0} C to 40^{0} C$ . The thermal capacity of each calorimeter is numberically equal to the volume of either liquid. The specific gravity of alcohol is 0.8. If the specific heat capacity of water is 1 cal/gm, the specific heat capacity of alcohol will be

Moderate

A

0.6 $cal / gm -^{0} C$
B

0.8 $cal / gm -^{0} C$
C

1.6 $cal / gm -^{0} C$
D

1.8 $cal / gm -^{0} C$

Solution

Let V be the volume of either liquid
Thermal capacity of each calorimeter is V cap per $^{0} C$
Mass of water = V $\times 1 = V g$
Mass of alcohol = V $\times 0.8 = 0.8 Vg$
Rate of colling of water,
= $\frac{1}{100} [V (50 - 40) + V \times 1 \times (50 - 40)] = \frac{V}{5} cal / \sec$
Rate of cooling of alcohol
= $\frac{1}{74} [V (50 - 40) + S \times 0.8 V \times 10]$
= $\frac{1}{74} [10 V + 8 V \times S]$
Now $\frac{1}{74} [10 V + 8 V \times S] = \frac{V}{5}$
$∴ s = 0.6 cal / g^{0} C$

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